On the splitting fields of generic elements in Zariski dense subgroups

Let G be a connected, absolutely almost simple, algebraic group defined over a finitely generated, infinite field K  , and let Γ be a Zariski dense subgroup of G(K)G(K). We show, apart from some few exceptions, that the commensurability class of the field FF given by the compositum of the splitting fields of characteristic polynomials of generic elements of Γ determines the group G up to isogeny over the algebraic closure of K.